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So, in the end you get 4 formulas (for the ring and the disc) which calculate the stresses (tangential and radial) as a function of the angular speed.

The second question is to determine the angular velocity when the ring seperates from the disc. I am wondering in what kind of situation the ring seperates from the disc because this is not clear to me. Is it because of a displacement of the inner edge of the ring for example?